Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 17
... units of feet , inches , miles , meters , or smoots . * In any calculation to eliminate possible confusion only one unit of length should be used . In this text we will use metric units in the m - k - s system , i.e. , meters for length ...
... units of feet , inches , miles , meters , or smoots . * In any calculation to eliminate possible confusion only one unit of length should be used . In this text we will use metric units in the m - k - s system , i.e. , meters for length ...
Page 44
... unit vectors which not only have fixed magnitude but also have fixed directions . ) In polar coordinates ( centered at the fixed vertex of the pendulum ) , the position vector is pointed outward with length L , = Lî , ( 14.1 ) where is ...
... unit vectors which not only have fixed magnitude but also have fixed directions . ) In polar coordinates ( centered at the fixed vertex of the pendulum ) , the position vector is pointed outward with length L , = Lî , ( 14.1 ) where is ...
Page 276
... unit time crossing at x = a ( moving to the right ) minus the number of cars per unit time crossing ( again moving to the right ) at x = b , or = dN dt = q ( a , t ) — q ( b , t ) , ( 60.2 ) since the number of cars per unit time is the ...
... unit time crossing at x = a ( moving to the right ) minus the number of cars per unit time crossing ( again moving to the right ) at x = b , or = dN dt = q ( a , t ) — q ( b , t ) , ( 60.2 ) since the number of cars per unit time is the ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
NEWTONS LAW AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
analyze approximation Assume c₁ c₂ calculated conservation of cars Consider corresponding d2x dt2 de/dt density wave velocity depends derived determine dq/dp dx dt dx/dt equilibrium population equilibrium position equilibrium solution example exercise exponential Figure flow-density force formula friction function growth rate highway increases initial conditions initial density initial traffic density initial value problem integral intersect isoclines logistic equation mass mathematical model maximum method of characteristics motion moving Newton's nonlinear pendulum number of cars observer occurs ordinary differential equation oscillation P/Pmax P₁ partial differential equation period phase plane Pmax potential energy problem qualitative region result sharks shock velocity Show shown in Fig simple harmonic motion Sketch the solution sketched in Fig slope solve species spring spring-mass system stable straight line Suppose Taylor series tion traffic flow traffic light trajectories Umax Umaxt unstable equilibrium variables velocity-density x₁ yields zero др